Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/17692
Title: 
Graph-functions associated with an edge-property
Authors: 
Issue Date: 
2004
Citation: 
Dong, F., Hendy, M., Teo, K. L., & Little, C. H. C. (2004). Graph-functions associated with an edge-property. Australasian Journal of Combinatorics, 30, 3-20.
Abstract: 
Let P be an edge-property of graphs. For any graph G we construct a polynomial Ψ(G, η,P), in an indeterminate η, in which the coefficient of ηr for any r ≥ 0 gives the number of subsets of E(G) that have
cardinality r and satisfy P. An example is the well known matching polynomial of a graph. After studying the properties of Ψ(G, η,P) in general, we specialise to two particular edge-properties: that of being an
edge-covering and that of inducing an acyclic subgraph. The resulting polynomials, called the edge-cover and acyclic polynomials respectively, are studied and recursive formulae for computing them are derived. As
examples we calculate these polynomials for paths and cycles.
URI: 
ISSN: 
1034-4942
Website: 
Appears in Collections:Journal Articles

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